Rock anisotropic wave velocity characterization and acoustic emission location optimization based on Lodrigues matrix

In order to investigate the anisotropy characteristics of rock wave velocity and its influence on acoustic emission location accuracy, uniaxial compression tests of marble and siltstone were carried out. Before the peak, the marble is almost completely in the elastic stage, the average wave velocity remains basically unchanged, and the horizontal wave velocity is always greater than the oblique longitudinal wave velocity, indicating that the longitudinal cracks are less in the initial state. In siltstone compaction stage, the horizontal, oblique longitudinal and average wave velocity all show an increasing trend. In the elastic stage, the horizontal wave velocity and the average wave velocity decrease slowly, which indicates that the rock has a small fracture in the longitudinal stage. In the damage stage, the horizontal, oblique longitudinal and average wave velocity decrease rapidly, indicating that the fracture has been penetrated. According to the characteristics of rock wave velocity evolution in different directions, a three-dimensional ellipsoid characterization method of rock anisotropic wave velocity based on Lodrigues matrix is proposed. The statistical ellipsoid azimuth of the ellipsoid is consistent with the true crack distribution, and more than 77% of the long-axis azimuth of marble and siltstone wave velocity ellipsoid is consistent with the crack distribution, indicating that the method can be applied to crack propagation prediction. An acoustic emission location method combined with anisotropic wave velocity evolution characteristics is proposed. The average error of the proposed method is determined to be 1.89mm in marble and 2.76mm in siltstone by lead breaking test. Compared with the traditional simplex method and Geiger method, the positioning accuracy of this method is increased by more than 58% in both rocks, which verifies the accuracy of the proposed location method.